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  • Need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 51

Need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 51

Answers (1)

Answer: 120

Hint: To solve this equation we use \frac{d}{dx}uvwz   form

Given: \begin{aligned} &f(x)=(1+x) \cdot\left(1+x^{2}\right) \cdot\left(1+x^{4}\right)\left(1+x^{8}\right)\\ \end{aligned}

                                u                v                   w                z

Solution:

          \frac{d}{d x}(u v w z)=v w z \cdot \frac{d u}{d x}+u w z \cdot \frac{d v}{d x}+u v z \cdot \frac{d w}{d x}+u v w \frac{d z}{d x}

        \begin{array}{r} f^{\prime}(x)=1 \times\left(1+x^{2}\right)\left(1+x^{4}\right)\left(1+x^{8}\right)+(1+x)\left(1+x^{4}\right)\left(1+x^{8}\right) 2 x+ \\ (1+x)\left(1+x^{2}\right)\left(1+x^{8}\right) 4 x^{3}+8 x^{7}(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right) \end{array}

        \begin{aligned} &f^{\prime}(1)=1 \times 2 \times 2 \times 2+2 \times 2 \times 2 \times 2+2 \times 2 \times 2 \times 4+8 \times 1 \times 2 \times 2 \times 2 \\\\ &=8+16+36+64 \\\\ &f(1)^{\prime}=120 \end{aligned}

 

 

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